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        <title>API docs for &ldquo;sympy.functions.special.polynomials.chebyshevu&rdquo;</title>
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        <body><h1 class="class">Class s.f.s.p.chebyshevu(<a href="sympy.functions.special.polynomials.PolynomialSequence.html">PolynomialSequence</a>):</h1><span id="part">Part of <a href="sympy.functions.special.polynomials.html">sympy.functions.special.polynomials</a></span><div class="toplevel"><div><p>chebyshevu(n, x) gives the nth Chebyshev polynomial of the second kind 
of x, U_n(x)</p>
<p>The Chebyshev polynomials of the second kind are orthogonal on [-1, 1] 
with respect to the weight sqrt(1-x**2).</p>
<h1 class="heading">Examples</h1>
<pre class="py-doctest">
<span class="py-prompt">&gt;&gt;&gt; </span>x = Symbol(<span class="py-string">'x'</span>)
<span class="py-prompt">&gt;&gt;&gt; </span>chebyshevu(0, x)
<span class="py-output">1</span>
<span class="py-output"></span><span class="py-prompt">&gt;&gt;&gt; </span>chebyshevu(1, x)
<span class="py-output">2*x</span>
<span class="py-output"></span><span class="py-prompt">&gt;&gt;&gt; </span>chebyshevu(2, x)
<span class="py-output">(-1) + 4*x**2</span></pre>
</div></div><table class="children"><tr class="function"><td>Function</td><td><a href="#sympy.functions.special.polynomials.chebyshevu.calc">calc</a></td><td><span class="undocumented">Undocumented</span></td></tr></table>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.functions.special.polynomials.chebyshevu.calc">calc(n, prev):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div></body>
        